Regular water waves have wavelength 12 m and frequency 0.40 Hz. They approach two harbour entrances of width 6 m and 30 m. (a) Calculate wave speed and period. [3] (b) Compare the expected diffraction at the two entrances. [3] (c) Explain how a two-dimensional wavefront sketch should differ behind each entrance. [2] (d) State two limits of applying this simple model to a real harbour. [2]

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Wave speed is 4.8 m/s and period is 2.5 s. The 6 m gap is narrower than one wavelength and produces strong spreading; the 30 m gap is 2.5 wavelengths wide and produces less spreading. (a) Wave speed v = fλ = 0.40 × 12 = 4.8 m/s. The period is T = 1/f = 1/0.40 = 2.5 s. (b) For the 6 m entrance, width/wavelength = 6/12 = 0.50, so diffraction is strong and energy spreads through a broad range of directions. (b) For the 30 m entrance, width/wavelength = 30/12 = 2.5, so most wavefronts continue roughly forward with only edge spreading. Diffraction is not literally zero. (c) Behind 6 m, draw widely curved, nearly semicircular fronts with 12 m separation. Behind 30 m, draw a broad central region of straighter fronts and curvature mainly near both edges. (d) Real seas contain many frequencies and directions, while water depth changes wave speed. Reflection from walls, irregular entrances, wind and breaking also violate the simple uniform-wave model.

Predict waves entering two harbour gaps

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